The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did…

The ability to successfully discriminate between multiple potentially relevant source analogs when solving new problems is crucial to proficiency in a mathematics domain. Experimental findings in two different mathematical contexts demonstrate that providing cues to support comparative reasoning during an initial instructional analogy, relative to…

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is, what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is…

American students continue to struggle on measures of student achievement. This study employed Hierarchical Linear Modeling to estimate a two-level model and examine the influences of calculator use and teachers' instructional practices on student achievement in mathematics amongst first-grade students. The outcome variable was mathematics test…

The equal sign is perhaps the most prevalent symbol in school mathematics, and developing an understanding of it has typically been considered mathematically straightforward. In fact, after its initial introduction during students' early elementary school education, little, if any instructional time is explicitly spent on the concept in the later…

The study presented in this paper seeks to investigate the impact of authenticity on the students' disposition to make necessary real world considerations in their word problem solving. The aim is also to gather information about the extent to which different reasons for the students' behaviors are responsible for not providing solutions that are…

This study evaluates the effects of an intervention aimed at improving representational flexibility in linear-function problems. Forty-nine students aged 13-16 participated in the study. A pretest-intervention-posttest design with an experimental and control group was used. At pretest, both groups solved a choice test, where they could freely…

This paper reports on the potential roles and importance of electrooculography (EOG) for mathematics educational neuroscience research. EOG enables accurate measurements of eye-related behavior (i.e., blinks & movements) by recording changes in voltage potentials generated by eye-related behavior. We identify and discuss three main uses of EOG.…

This article is the second in a series of two papers which suggest some practical, spreadsheet-based ideas for helping students to make appropriate connections between particular algebraic concepts. Solving equations has traditionally been taught as a pen-and-paper process. Spreadsheets, such as that of Excel, provide a contemporary, and powerful…

Arithmetic word problems are often presented accompanied by illustrations. The present study examined how different types of illustrations influence the speed and accuracy of performance of both good (n = 67) and poor arithmeticians (n = 63). Twenty-four arithmetic word problems were presented with four types of illustrations with increasing…

The reality is that approximately 5-8% of school-age students have memory or other cognitive deficits that interfere with their ability to acquire, master, and apply mathematical concepts and skills (Geary, 2004). These students with Mathematical Learning Disabilities (MLD) are at risk for failure in middle school mathematics because they…

The authors explored the effects of teaching conceptual model-based problem-solving instruction on students' ability to solve problems in various situations. Participants were 3 4th-and 5th-grade students with or at risk for mathematics disabilities. The authors used an adapted multiple-probe across-participants design to assess the functional…

The projects Xmath (Bringslid and Canessa, 2002) and dMath (Bringslid, de la Villa and Rodriguez, 2007) were supported by the European Commission in the so called Minerva Action (Xmath) and The Leonardo da Vinci programme (dMath). The Xmath eBook (Bringslid, 2006) includes algorithms into a wide range of undergraduate mathematical issues embedded…

Hypothesis testing is one of the more difficult concepts for students to master in a basic, undergraduate statistics course. Students often are puzzled as to why statisticians simply don't calculate the probability that a hypothesis is true. This article presents an exercise that forces students to lay out on their own a procedure for testing a…

US and China are reforming mathematics teaching by shifting from students' attainment of facts and procedures toward development of competencies in reasoning, communication, connections, and problem solving, and application of these in real life contexts. Differences in students' overall performance, curricula, and teachers' knowledge and…